Surveys in Differential Geometry

Volume 11 (2006)

Perelman’s Stability Theorem

Pages: 103 – 136



Vitali Kapovitch (Department of Mathematics, University of Toronto, Toronto, Ontario M5S2E4, Canada)


We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence $X_i$ of Alexandrov spaces with $\curv$ $\ge k$ Gromov-Hausdorff converging to a compact Alexandrov $X$, $X_i$ is homeomorphic to $X$ for all large $i$.

Full Text (PDF format)